We report Grand Canonical Monte Carlo (GCMC) simulation studies of the adsorption and heat of adsorption of simple inert gases in two model microporous materials: aluminophosphates (AℓPO4-5, AℓPO4-8 and VPI-5) and alumina-pillared clays. The intermolecular potentials are spherical Lennard-Jones for both the fluid-fluid and fluid-solid interactions; both structured and structureless walls are considered. For argon in VPI-5 and AℓPO4-5 we find qualitative agreement with experiment, but the predicted maximum adsorption is about 20% higher than that obtained experimentally; possible reasons for this discrepancy are discussed. For the pillared clays we find a first order phase transition below some critical pillar density. This finding seems to be in qualitative agreement with existing experimental data.